Related papers: Uniform asymptotic approximation of diffusion to a…
A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have…
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
Diffusion-limited reactions (DLR) are usually described within the Smoluchowski theory, which neglects interactions between the diffusing components. We propose a first extension of such frame- work that incorporates excluded-volume…
The question addressed here is the long time evolution of the solutions to a class of one-dimensional reaction-diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation, discussed in the first…
The reaction-diffusion master equation (RDME) is a lattice stochastic reaction-diffusion model that has been used to study spatially distributed cellular processes. The RDME is often interpreted as an approximation to spatially-continuous…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
This chapter aims at emphasizing the crucial role of partial reactivity of a catalytic surface or a target molecule in diffusion-controlled reactions. We discuss various microscopic mechanisms that lead to imperfect reactions, the Robin…
The replicator equation is ubiquitous for many areas of mathematical biology. One of major shortcomings of this equation is that it does not allow for an explicit spatial structure. Here we review analytical approaches to include spatial…
A general topic of current interest is the analysis of diffusion problems in singularly perturbed domains with small interior targets or traps (the narrow capture problem). One major application is to intracellular diffusion, where the…
Chemical reactions involving diffusion of reactants and subsequent chemical fixation steps are generally termed "diffusion-influenced" (DI). Virtually all biochemical processes in living media can be counted among them, together with those…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
Many processes in cell biology involve diffusion in a domain $\Omega$ that contains a target $\calU$ whose boundary $\partial \calU$ is a chemically reactive surface. Such a target could represent a single reactive molecule, an…
The behavior of the single-species reaction process $A+A\to O$ is examined near an impenetrable boundary, representing the flask containing the reactants. Two types of dynamics are considered for the reactants: diffusive and ballistic…
The paper is to study the asymptotic dynamics in nonmonotone comparable almost periodic reaction-diffusion system with Dirichlet boundary condition, which is comparable with uniformly stable strongly order-preserving system. By appealing to…
Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…